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A209580 Triangle of coefficients of polynomials v(n,x) jointly generated with A209579; see the Formula section.

%I A209580 #6 Mar 30 2012 18:58:15
%S A209580 1,2,2,2,4,3,3,7,8,4,3,11,19,15,5,4,15,34,43,26,6,4,21,57,91,87,42,7,
%T A209580 5,26,87,176,217,163,64,8,5,34,126,301,473,472,288,93,9,6,40,176,489,
%U A209580 908,1150,954,485,130,10,6,50,235,745,1626,2460,2587,1817,784
%N A209580 Triangle of coefficients of polynomials v(n,x) jointly generated with A209579; see the Formula section.
%C A209580 Alternating row sums:  1,0,1,0,1,0,1,0,1,0,...
%C A209580 For a discussion and guide to related arrays, see A208510.
%F A209580 u(n,x)=x*u(n-1,x)+v(n-1,x),
%F A209580 v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F A209580 where u(1,x)=1, v(1,x)=1.
%e A209580 First five rows:
%e A209580 1
%e A209580 2...2
%e A209580 2...4....3
%e A209580 3...7....8....4
%e A209580 3...11...19...15...1
%e A209580 First three polynomials v(n,x): 1, 2 + 2x , 2 + 4x + 3x^2.
%t A209580 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209580 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
%t A209580 v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A209580 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209580 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209580 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209580 TableForm[cu]
%t A209580 Flatten[%]   (* A209579 *)
%t A209580 Table[Expand[v[n, x]], {n, 1, z}]
%t A209580 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209580 TableForm[cv]
%t A209580 Flatten[%]   (* A209580 *)
%Y A209580 Cf. A209579, A208510.
%K A209580 nonn,tabl
%O A209580 1,2
%A A209580 _Clark Kimberling_, Mar 11 2012